5 research outputs found
Chern-Simons Reduction and non-Abelian Fluid Mechanics
We propose a non-Abelian generalization of the Clebsch parameterization for a
vector in three dimensions. The construction is based on a group-theoretical
reduction of the Chern-Simons form on a symmetric space. The formalism is then
used to give a canonical (symplectic) discussion of non-Abelian fluid
mechanics, analogous to the way the Abelian Clebsch parameterization allows a
canonical description of conventional fluid mechanics.Comment: 12 pages, REVTeX; revised for publication in Phys Rev D; email to
[email protected]
Creation and evolution of magnetic helicity
Projecting a non-Abelian SU(2) vacuum gauge field - a pure gauge constructed
from the group element U - onto a fixed (electromagnetic) direction in isospace
gives rise to a nontrivial magnetic field, with nonvanishing magnetic helicity,
which coincides with the winding number of U. Although the helicity is not
conserved under Maxwell (vacuum) evolution, it retains one-half its initial
value at infinite time.Comment: Clarifying remarks and references added; 12 pages, 1 figure using
BoxedEPSF, REVTeX macros; submitted to Phys Rev D; email to
[email protected]
Conservation laws of scaling-invariant field equations
A simple conservation law formula for field equations with a scaling symmetry
is presented. The formula uses adjoint-symmetries of the given field equation
and directly generates all local conservation laws for any conserved quantities
having non-zero scaling weight. Applications to several soliton equations,
fluid flow and nonlinear wave equations, Yang-Mills equations and the Einstein
gravitational field equations are considered.Comment: 18 pages, published version in J. Phys. A:Math. and Gen. (2003).
Added discussion of vorticity conservation laws for fluid flow; corrected
recursion formula and operator for vector mKdV conservation law
Perfect Fluid Theory and its Extensions
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian
formulations. The theory is related to a description of extended structures in
higher dimensions. Internal symmetry and supersymmetry degrees of freedom are
incorporated. Additional miscellaneous subjects that are covered include
physical topics concerning quantization, as well as mathematical issues of
volume preserving diffeomorphisms and representations of Chern-Simons terms (=
vortex or magnetic helicity).Comment: 3 figure
Knotty inflation and the dimensionality of spacetime
We suggest a structure for the vacuum comprised
of a network of tightly knotted/linked flux tubes formed in a QCD-like cosmological phase transition and show that such a network can drive cosmological inflation. As the network can be topologically stable only in three space dimensions, this scenario provides a dynamical explanation for the existence of exactly three large spatial dimensions in our Universe